Annals of Pure and Applied Logic 103 (1-3):39-53 (2000)

Abstract
We construct a G δ set G ⊆ ω ω ×2 ω with null vertical sections such that each perfect set P ⊆2 ω meets almost all vertical sections of G in the following sense: we can define from P subsets S of ω of density zero such that whenever the section determined by x ∈ ω ω does not meet P , then x ∈ S for all but finitely many i . This generalizes theorems of Mokobodzki and Brendle et al. 185–199)
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DOI 10.1016/s0168-0072(99)00018-4
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References found in this work BETA

Combinatorial Properties of Hechler Forcing.Jörg Brendle, Haim Judah & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (3):185-199.
Jumping with Random Reals.Tomek Bartoszynski & Haim Judah - 1990 - Annals of Pure and Applied Logic 48 (3):197-213.
Around Random Algebra.Haim Judah & Saharon Shelah - 1990 - Archive for Mathematical Logic 30 (3):129-138.

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